Over the years, my dogs have gotten into a lot. 90% of the time, they have gotten into something dead on one of our hikes.t
I tend to stop feeding and closely monitor water intake and output / restrict to something reasonable if needed.
As soon as the diarrhea stops, I start to feed white rice + boiled chicken in small quantities.
In general, dogs can handle random bacteria better than humans. Sometimes they just need to slow down their food and water intake to let their digestive tract settle down.
If the issue does not look like it is resolving within 24-36 hours, I contact the vet. But this is based on 45 plus years of rambling with dogs.
I am lucky, we don't have nuisance rodents in my area. So poisoning is extremely rare. Almost all the blufflands we hike is owned by conservation groups. It is too rugged to farm or develop.